Quadratic optical response to a magnetic field in the layered magnet CrSBr

The optical properties of layered materials are dominated by intralayer excitons; especially for layered antiferromagnets the layer-to-layer charge hopping, and therefore interlayer excitons, are spin forbidden. An external magnetic field, however, can continuously drive the magnetic order towards layer-to-layer ferromagnetic, which opens spin-allowed charge-transfer channels between the layers. Here, we elaborate how their admixture changes the composition and nature of the excitons, leading to an extension over many layers, and causing a quadratic redshift with respect to the external magnetic field in CrSBr. We present a minimal four-band model to elucidate the interplay between the various interaction and coupling mechanisms which is able to reproduce the findings of our <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>G</a:mi><a:mi>W</a:mi></a:mrow></a:math>–Bethe-Salpeter equation calculations as a function of magnetic field. Our model is generally valid for any coupled layers with different spin directions and the insights help to systematically address excitons and to predict their optical signatures in such systems.